Holographic Principle -towards the new paradigm- Bum-Hoon Lee Center for Quantum Spacetime(CQUeST)/Dept. of Physics Sogang University Seoul, Korea

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1 Holographic Principle -towards the new paradigm- Bum-Hoon Lee Center for Quantum Spacetime(CQUeST)/Dept. of Physics Sogang University Seoul, Korea AKPA-IBS May 9, 2014

2 I. Introduction : Motivation & Basics Q : How to understand the nonperturbative physics of the strongly interacting systems? Ex) In QCD, how to explain confinement, chiral symmetry breaking, phases (with or w/o chemical potential), meson spectra etc.? Ex) How to understand the phenomena in the Strongly correlated condensed matter systems? AdS-CFT Holography : 3+1 dim. QFT 4+1 Classical Gravity Theory Useful tool for strongly interacting systems such as QCD, Composite (Higgs) particles?, Condensed Matter, etc.

3 Contents I. Introduction Motivation and Basics String theory as a tool for the strongly interacting systems II. Holography Principle - AdS/CFT III. Application of the Holographic Principle 1. AdS/QCD 2. AdS/CMT 3. Application to Nonequilibrium Physics IV. Summary

4 2 nd revolution of the string theory (1994) (Ex: p = 3) (Classical) Gravity Theory Anti de Sitter (AdS) Space in (p+1)+1 dimension QFT(open string) Gravity(clsoed string) 5Dim. Spacetime time radial space time 5 th radial direction 4Dim. SpaceTime (Quantum) Field Theory Conformal Field Theory (CFT) in p+1 dimension 4

5 Main idea on holography through the Dp branes Dp-brane carry tension(energy) and charges (for p+2 form) Dp brane s low E dynamics by fluctuating Open Strings SUGRA on AdS (p+2) space Dp-branes #Dp-branes = Nc = (p+1)dim. SU(Nc) SYM (0, 1,, p) Question : 4 = 5? 3+1 dim. QFT (large Nc) 4+1 dim. Effective Gravity description (p+1,, 9) Naïve Answer : Coupling constants are running in QFT! Energy scale in QFT corresponds to the parameter in extra dimension or radial direction in AdS5 space

6 4Dim QFT Perturbative : Easy Nonperturbative : Hard 5Dim parameter Quantum Gravity : Hard Classical Gravity : Easy New Methodolgoy : 4can use the 5 dim. classical gravity description for the 4dim. strongly interacting system. 6

7 4d QFT(on boundary ) 5d Gravity (in bulk ) Parameter (, ) (, ) Ex) Nc of D3 branes N=4 SU(Nc) SYM SUGRA on AdS5 x S5 Comments N=4 SU(Nc) SYM SUGRA on AdS5 x S5 Nc of D3 branes In Anti-deSitter Space (, ) (, ) In asymptotic AdS Space (ex) QCD?? (in asymptotic AdS Space)

8 Intersecting D-Branes Flavors, mesons, etc. Ex) D3-D7 Strings Low energy dynamics CPX 3-3 : Aμ, Φ, λ, χ 0,1,2,3 (N=2 Vector multiplet in adjoint N=2 SYM with #M hyper #N : Q, ~, Q ψ, ~ 4 #M (N=2 Hypermultiplet matter in fundamental) Still far from QCD! Extension of the AdS/CFT the gravity theory on the asymptotically AdS space -> modified boundary quantum field theory (nonconf, less SUSY, etc.) Gravity w/ black hole background corresponds to the finite T field theory

9 Radial coord. r in the bulk is proportional to the energy scale E of QFT AdS/CFT Dictionary Witten 98; Gubser,Klebanov,Polyakov 98 Parameters (, ) (, ) Partition function of bulk gravity theory (semi-classial) Generating functional of bdry QFT for operator = bdry value of the bulk field : source of the bdry op. : scalar, Correlation functions by 5D bulk field Ф(t, x, u) Operator (t, x) w/ 5D mass w/ Operator dimesion 5D gauge symmetry Current (global symmetry)

10 (Operator in QFT) <-> (p-form Field in 5D) : Conformal dimension : mass (squared) Ex) Gluon cond. dilaton baryon density vector w/ U(1) fields in gravity massless dilaton scalar field with m=0 vector field gauge group in the dual operators of QCD gluon condensation chiral condensation mesons in the flavor group

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12 III. Application Needs the dual geometry!. Approaches : Top-down Approach : rooted in string theory Find brane config. or SUGRA solution giving the gravity dual (May put the probe brane) Ex) Nc of D3(D4) + M of D7(D8), 10Dim. SUGRA solution etc. Bottom-up Approach:phenomenological Introduce fields, etc. (as needed based on AdS/CFT) 5D setup 4D effective Lagrangian

13 1. AdS/QCD (Holographic QCD) Witten 98 Goal : Using the 5 dim. dual gravity, study 4dim. strongly interacting QCD such as spectra & Phases, etc. parameters (Nc, Nf, mq, T and μ, χ-symm., gluon condensation, etc.) Ex) finte temperature for the pure Yang-Mills theory without quark matters Low T Confinement QCD Phase transition Hawking-Page transition =Transition of bulk geometry High T Deconfinement QCD (4Dim) Hadron Quark-Gluon Gravity (5Dim) Thermal AdS AdS Black Hole Hawking-Page phase transition [ Herzog, Phys.Rev.Lett.98:091601,2007 ] The geometry is described by the following action : cosmological constant The geometry with smaller action is the stable one for given T. > 0 for T < Tc < 0 for T>Tc

14 Holographic QCD for finite chemical potential Low T QCD Phase transition High T Confinement Deconfinement QCD (4Dim) Hadron Quark-Gluon Gravity (5Dim) thermal & charged AdS RNAdS Black Hole Hawking-Page transition (q = 0) (BHL, Park,Sin JHEP 0907,(2009)) Gravity (5Dim) Thermal AdS AdS Black Hole

15 For the fixed chemical potential dimensionless variables For the fixed number density Legendre transformation, the Hawking-Page transition occurs at

16 Light meson spectra in the hadronic phase Jo, BHL, Park,Sin JHEP 2010, arxiv: Turn on the fluctuation in bulk corresponding the meson spectra in QCD X is the dual to the quark bilinear operator <qbar q >. 1. Vector meson 2. Axial vector meson 3. pion

17 Chiral Condensate Effect (w/ & w/o Density Effect) The gravity action in the bulk is C. Park, B-HL, S. Shin, arxiv: We set The background geometries of our interest are obtained from a gravity action with the massive scalar field and U(1) gauge interaction. an ansatz for the asymptotic AdS metric in the Fefferman-Graham coordinate as We take R = 1. M = 1, 2, 3, z

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19 2. AdS/CMT Temperature d dim. CMT SC phase Normal Phase d+1 dim. 중력 AdS Black Hole with hair AdS Black Hole no hair Goal : Holographic Explanation for phenomena in the strongly correlated condensed matter systems, such as superconductivity, non Fermi liquid, Strange Metal, etc. 19

20 3.Holographic Approach to the nonequilibrium physics Blue routes : Condensation Process Red routes: Quantum Quenching - Phase transition in real time!

21 X. Bai, B-HL, M.Park, and K. Sunly arxiv:

22 Temperature d dim. CMT SC phase Normal Phase d+1 dim. Gravity Black Hole with hair Black Hole no hair 22

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24 IV. Summary Holographic Principles ( through the D-brane configuration) (d+1 dim.) (classical) Sugra (d dim.) (quantum) YM theories SUGRA w/ BH Finite Temperature Constructing the dual geometry : Top-down & Bottom-up Holographic QCD - w/o chemical potential - phase : confined phase deconfined phase transition Geometry : thermal AdS AdS BH Hawking-Page transition - in dense matter - (U(1) chemical potential baryon density ) deconfined phase by RNAdS BH hadronic phase by tcads Hawking-Page phase transition T deconfined Quark-Gluon Hadron confined

25 IV. Summary - continued AdS/CMT Holographic principle can also be applied to the nonequilibrium physics Holographic Principle may provide a new methodology for the strongly interacting phenomena! String Theory may provide the new paradigm for the theoretical physics in 21 st Century

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